Calculus III / Multivariable Calculus
Time: Tues, Thurs, Fri 4-6 pm; Weds 5-6 pm
After completing the entire course, I have to say Math 200 wasn’t that hard. It definitely seemed harder during the course as opposed to after the course. I’m probably going to get the same mark in this course that I got in Math 103 last semester. So I would say Math 200 is slightly harder than Math 103. Math 200 had an overall average of 67.11% in 2009S and 67.43% in 2009W. In both cases, the top 28-29% of the class will achieve at least 80%. I tend to look at this statistic (what % of the class achieves 80% or higher) to tell how easy it is to get a high mark. I do this because I don’t want to take a course, especially as a GPA booster where the average mark is like 75% but the highest mark is only like 86%. Why? Because this means it’s easy to get a high B or low A but anything above that becomes unbelievably hard. Since I took the Math 200 in the first term of the Summer Session 2010, my classes were usually 2 hours in duration, with four classes a week. I had a one hour class on Wednesday, and that class was specifically for writing midterms.
The course material includes stuff like vectors, partial derivatives, chain rule, directional derivatives, max/min, Lagrange multipliers, and double/triple integrals. It’s sort of like first year calculus but adding an extra dimension (or more) and then you also learn a few completely new “useful” things.
I’d say that the difficulty of the material increases as the course progresses, which makes triple integrals (one of) the hardest topic, I guess. Since the length of the course during the summer is shortened, we didn’t have any homework which means that you don’t really get any feedback aside from the midterms. There were four midterms, once a week with the lowest midterm mark being omitted (yay, goodbye to the 67% midterm). The first midterm (mostly on the subject of vectors and planes) was definitely the easiest one out of the four.
People seemed to have a lot of trouble with certain topics:
1) Contour map drawing (drawing on the same coordinate grid several sketches of a function z = f(x, y) for particular constant values of z)
2) Finding derivatives of functions that are not explicitly defined
3) Setting the partial derivative of a function to zero and finding critical points (particularly because the algebra and arithmetic can get quite nasty)
4) Lagrange multipliers, especially with inequality constraints (sometimes you have to solve a system of linear equations in five variables)
You probably won’t understand what I just said until you start the course, but take note of these key areas so that you pay extra attention when you come across them.
The coursework for Math 200 I’d say is definitely doable: one simply needs to put in the effort to pay attention in class and also do the homework properly, whilst getting help whenever necessary. Unfortunately, I failed in achieving my goal to visit the professor at least once during this course, which I regretted…
Unfortunately, I would say that the recommended problems (from the textbook) were insufficient, as were the practice midterms. In fact, the prof simply took questions from the textbook for the practice midterms, and therefore the practice midterms were somewhat redundant and not extremely helpful. Such practice midterms brought about a false sense of security/preparedness.
I tried to review my notes after each lecture, and I think that helped me grasp the concepts enough to do practice problems. Practicing a variety of different problems for each topic is definitely one of the keys to success in this course, or perhaps in most Math courses. You never know what questions you’ll get on a midterm. To study for the midterms/final, I simply read my notes and made sure I understood them, and then I did problems in the textbook after each class. Although I said they didn’t always represent the questions you would find on a midterm, it was still useful to do. I would then follow up by doing midterms/finals from previous years.
Fortunately, our prof posted lecture slides, which is great for people who miss class “accidentally” or who are genuinely ill. It also helps those who want to check their notes after class for mistakes, and for the students who prefer listening to professor during lecture to concentrate on absorbing the information rather than copying stuff down without really understanding what one is writing. I prefer writing notes during class, but it was quite difficult to keep up with this professor’s speed (he was writing using Windows Journal on some sort of Tablet PC or something).
Also, the lecture notes were almost completely based off the textbook notes, which means it is easy to review only using the textbook. This also means that it is very easy to “self-study” for Math 200. What I mean by that is that you can just go get the textbook and read through the relevant sections (a list of the relevant sections can be easily found via Google) and do the relevant problems so that the next semester when you do take the course, it’ll kind of be like a repeat and you would probably be more prepared than the vast majority of your peers. This would definitely help for some people who take a longer time to learn. I was actually trying to learn the material from the book before each lecture, and it worked well but I got lazy and stopped.
The Final Exam: My final was 2.5 hours in duration and I believe the exam was about 11 pages long. To be honest, the final exam was significantly easier than I had anticipated and definitely much easier than those stupid killer midterms. I didn’t manage to check over all the questions – only 7 out of 8 of the questions – but nonetheless there was plenty of time. (The questions are often multi-part.) A downfall to taking this course in the summer is that the final exam was very soon after the course ended. For me, the official last day of the course was on a Friday, and the final exam was actually on Saturday. Furthermore, they almost made it late Friday instead of Saturday but chose not to. So I guess there’s not that much time to study between the end of the course and the final exam.
So, the textbook. When I took this course (2010S), the 6th edition of the textbook Multivariable Calculus by James Stewart was recommended. Since the course duration was so short (in the summer), I simply borrowed the book from the library (VPL) a week or two ahead of time to avoid other people borrowing it first. However, someone requested to hold it so I had to return it partway through the course and then I borrowed the textbook Early Transcendentals by the same author from my friend instead.
The material in both Multivariable Calculus and Early Transcendentals is essentially the same, with a few subtle differences here and there in the example problems and also in the practice problems. The same goes for differences between different versions. Although the 6th edition is recommended, I used a 5th edition and it worked perfectly fine. There isn’t really a benefit in using one over the other, aside from maybe that if you have the recommended textbook then the professor might be able to help you better (since he has the same textbook to refer to, presumably). Since I’ve used both textbooks, I can safely say that you’ll get the same thing out of either one you use. If you took a course such as Math 100/101 in a previous semester that used Early Transcendentals, then I would just keep it for Math 200.
Unfortunately, the student solutions manual that comes with Early Transcendentals does not cover the chapters that are relevant to Math 200. (By the way, the chapter numbers were off between the two books. For example, Chapter 15 in one book will be Chapter 14 in the other, etc.) Therefore, if you want to have access to a solutions manual, you will have to go get another one that covers the relevant topics. As for me, I simply went to the UBC bookstore on several occasions before class, and compared my answers for questions I was confused about to those in the solutions manual. However, I must say that this was somewhat inconvenient and I would definitely consider having access to a copy of the solutions manual from home next time, but at least I saved more money. There is also a study guide you can purchase for the textbook by the same author. I looked through it (briefly, though), it didn’t seem that useful to be honest. I believe there’s just a bunch of examples with solutions and a few notes here and there. I wouldn’t recommend purchasing it, unless you have a lot of time to dedicate to Math 200 AND you think it’d actually come in handy. There are already examples from class notes and from the actual textbook, and plenty of problems in the textbook as well whose complete solutions may be found in the solutions manual. For those who would consider buying it, I would recommend not buying it right away, but waiting a while (at least a week into the course) and then going to the bookstore to see how effective it would be as a study guide for the material you just learned.
Multivariable Calculus 6/E by James Stewart (Textbook only)
I bought for: N/A, borrowed from library.
UBC Bookstore cost: $153.35 new, $115 used.
4 pc PKG *CORE* Multivariable Calculus 6/E w/ Solutions Manual
UBC Bookstore cost: $154.80 new, $116 used
edit: Jan. 2011 Bookstore prices: $155.55 new
(Why is there essentially no cost difference from the textbook + solutions and just the textbook?)
Multivariable Calculus 6/E by James Stewart, Student Solutions Manual ONLY
I bought for: N/A, went to bookstore before class to compare answers.
UBC Bookstore cost: $59.10 new, $44.35 used
edit: Jan. 2011 Bookstore prices: $64.60 new, $48.45 used.
Multivariable Calculus 6/E by James Stewart, Study Guide ONLY
I bought for: N/A, it seems kinda useless.. and I’m too lazy to spend that much time.
UBC Bookstore cost: $44.90 new, $33.70 used
edit: Jan. 2011 Bookstore prices: $49.25 new, $36.95 used
I’ll also mention that at least for the summer, students in Math 253 attended the same lectures as those in Math 200. This means that some of my fellow classmates were actually getting credit for Math 253 despite the fact that we all wrote the same midterms and final exam.
I believe these two courses are separated in the Winter session.